Option pricing in stochastic volatility models driven by fractional Lévy processes

Abstract

In this paper, we propose a continuous time fractional stochastic volatility model which extends the Barndorff-Nielsen and Shephard (2001) (BNS) model. Our model is the fractional BNS model, where we model the volatility as a fractional Levy-driven Ornstein-Uhlenbeck process. We allow the memory parameter to be flexible so that our model can potentially produce short- or long-memory in volatility. We derive the analytical formula for option pricing using Fourier inversion technique. We numerically study the effect of memory parameter on the option prices and the calibration result indicates that the fractional model significantly improves the performance of the original BNS model.